The Design of Optimal Pay-as-Bid Procurement Mechanisms

60 Pages Posted: 2 Jun 2022 Last revised: 3 Jun 2022

See all articles by Je-ok Choi

Je-ok Choi

Stanford University - Institute for Computational and Mathematical Engineering

Daniela Saban

Stanford Graduate School of Business

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University

Date Written: May 31, 2022

Abstract

Problem definition: We consider the mechanism design problem of finding an optimal pay-as-bid mechanism in which the platform chooses an assortment of suppliers in order to balance the trade-off between two objectives: providing enough variety to accommodate heterogeneous buyers, yet at low prices.

Academic/practical relevance: Modern buying channels, including e-commerce and public procurement, often consist of a platform that mediates transactions. Frequently, these platforms implement simple and transparent mechanisms to induce suppliers' direct participation, which typically results in pay-as-bid (or first-price) mechanisms where suppliers set their prices.

Methodology: We introduce a novel class of assortment mechanisms that we call k-soft reserves (k-SRs): if at least k suppliers choose a price below the soft-reserve price, then only those suppliers are added to the assortment; otherwise, all the suppliers are added.

Results: We show the optimality of k-SRs for a class of stylized symmetric models in order to derive the intuition behind the mechanics of these mechanisms. Then, through extensive numerical simulations, we provide evidence of the robustness of k-SRs in more general and realistic settings.

Managerial implications: Our results give intuitive and simple-to-use prescriptions on how to optimize pay-as-bid assortment mechanisms in practice, with an emphasis on public procurement settings.

Keywords: mechanism design, pay-as-bid, market design, procurement, auctions, assortments

JEL Classification: D44, D47, D82

Suggested Citation

Choi, Je-ok and Saban, Daniela and Weintraub, Gabriel Y., The Design of Optimal Pay-as-Bid Procurement Mechanisms (May 31, 2022). Stanford University Graduate School of Business Research Paper, Available at SSRN: https://ssrn.com/abstract=3785023 or http://dx.doi.org/10.2139/ssrn.3785023

Je-ok Choi (Contact Author)

Stanford University - Institute for Computational and Mathematical Engineering ( email )

Huang Building, 475 Via Ortega
Suite 060 (Bottom level)
Stanford, CA 94305-4042
United States

Daniela Saban

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University ( email )

Stanford, CA 94305
United States

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